Your mother is completely, totally wrong.
You & your mother own the house as tenants in common, I assume. This means that either of you has a right to live in the house, but neither of you HAS to live there. In other words, mom cannot prevent you from living in the house, but she can't require you to live there either.
Any tenant in common owner can force the sale of a house. You go to court and file a motion for "partition by sale." Check the law or local library for form books and instructions on how to draft things and serve mom. The court will issue an order instructing you and your mother to put the house on the market at a reasonable price, and to accept a reasonable offer. (You don't have to accept the first offer, though.) After the house is sold and the commissions & expenses paid, the court will divide any money left over between you and your mom in proportion to your ownership.
If the deed does not say otherwise, you and your mom each own half the house.
Go to your county recorder's office and ask to see the deed filed on your house. You will need the parcel #. The deed will say whether you are tenants in common or joint tenants with right of survivorship. Joint tenants always own equal shares but can still sue for partition by sale the same as tenants in common.
You can move out and continue to pay your share of the mortgage, building up equity that you can borrow against later. You can move your significant other into the house with you. You can rent out the house (although there will be few takers, since mom can stay even if you rent). You can educate your mom on the real laws of co-ownership and try to work out something.
DO NOT quitclaim your portion of the house to your mother unless she refinances in her name only. You remain liable for the entire mortgage amount, whether your name is on the deed or not.
------------------
This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.